Water is an apparently simple molecule (H2O)
with a highly complex character. As a gas it is one of
lightest known, as a liquid it is much
denser than expected and as a solid it is
much lighter than expected. Much of the
behavior of liquid water is quite different from what is found with other
liquids, giving rise to the term 'the anomalous properties of water'.
a

As liquid water is so common-place in our everyday lives,
it is often regarded as a ‘typical’ liquid. In reality water is most
atypical as a liquid, behaving as a quite different material at low
temperatures to that when it is hot. It has often been stated (for
example, [127]) that life depends on these
anomalous properties of water. In particular, the large heat capacity,
high thermal conductivity and high water content in organisms contribute
to thermal regulation and prevent local temperature fluctuations, thus
allowing us to more easily control our body temperature. The high latent
heat of evaporation gives resistance to dehydration and considerable
evaporative cooling. Water is an excellent solvent due to its polarity,
high dielectric constant and small size, particularly for polar and ionic
compounds and salts.b It has
unique hydration properties towards
biological macromolecules (particularly proteins and nucleic acids) that
determine their three-dimensional structures, and hence their functions,
in solution. This hydration forms gels that can reversibly undergo the
gel-sol phase transitions that underlie many cellular mechanisms [351].
Water ionizes and allows easy proton exchange
between molecules, so contributing to the richness of the ionic
interactions in biology.

At 4°C water expands on heating OR cooling.
This density maximum together with the low ice density results in (i) the
necessity that all of a body of fresh water (not just its surface) is
close to 4°C before any freezing can occur, (ii) the freezing of rivers,
lakes and oceans is from the top down, so permitting survival of the
bottom ecology, insulating the water from further freezing, reflecting
back sunlight into space and allowing rapid thawing, and (iii) density
driven thermal convection causing seasonal mixing in deeper temperate
waters carrying life-providing oxygen into the depths. The large heat
capacity of the oceans and seas allows them to act as heat reservoirs such
that sea temperatures vary only a third as much as land temperatures and
so moderate our climate (for example, the Gulf stream carries tropical
warmth to northwestern Europe). The compressibility of water reduces the
sea level by about 40 m giving us 5% more land [65].
Water's high surface tension plus its
expansion on freezing encourages the erosion
of rocks to give soil for our agriculture.

Notable amongst the anomalies of water are the opposite properties of
hot and cold water, with the anomalous behavior more accentuated at low
temperatures where the properties of supercooled water often diverge from
those of hexagonal ice.c As cold
liquid water is heated it shrinks, it becomes
less easy to compress, its
refractive index increases, the
speed of sound within it increases, gases
become less soluble and it is
easier to heat and
conducts heat better. In contrast as hot liquid water is heated it
expands, it becomes easier to
compress, its
refractive index reduces, the speed of sound
within it decreases, gases become more soluble
and it is harder to heat and a poorer
conductor of heat. With increasing pressure,
cold water molecules move faster but hot
water molecules move slower. Hot water
freezes faster than cold water and ice
melts when compressed except at high
pressures when liquid water freezes when compressed.
No other material is commonly found as solid, liquid and gas.d

The anomalies of water appear as a heirarchy of effects with
different bounds [169]. These are shown
indicatively opposite as derived from modeling, not experimental data.
The ‘Structural’ bounds indicate where water is more disordered when
compressed, the ‘Dynamic’ bounds indicate where
diffusion increases with density, and the ‘Thermodynamic’
bounds show where there is a temperature of
maximum density; with the data from [169]
shifted upwards 38 K to give the correct temperature of maximum
density under standard pressure. As density always increases with
increasing pressure, a similar relationship holds with pressure along
the horizontal axis.

Water phase anomalies

Water has unusually high melting point.
[Explanation]

Water has unusually high boiling point.
[Explanation]

Water has unusually high critical point.
[Explanation]

Solid water exists in a wider variety
of stable (and metastable) crystal and amorphous structures than other
materials. [Explanation]

The thermal conductivity of ice reduces with increasing pressure. [Explanation]

The structure of liquid water changes at high pressure. [Explanation]

Supercooled water has two phases and a second
critical point at about -91°C. [Explanation]

Liquid water is easily supercooled but glassified with difficulty. [Explanation]

Liquid water exists at very low temperatures and freezes on heating.
[Explanation]

Liquid water may be easily superheated. [Explanation]

Hot water may freeze faster than cold water; the Mpemba effect. [Explanation]

Warm water vibrates longer than cold water. [Explanation]

Water density anomalies

The density of ice increases on heating (up to 70 K). [Explanation]

Water shrinks on melting. [Explanation]

Pressure reduces ice's melting point. [Explanation]

Liquid water has a high density that increases on heating (up to
3.984°C). [Explanation]

Pressure reduces the temperature of maximum density. [Explanation]

There is a minimum in the density of supercooled water. [Explanation]

Water has a low coefficient of expansion (thermal expansivity). [Explanation]

The graph uses data that have been scaled between
their maximum and minimum values (see original
data).

a Whether or not the properties of water are seen
to be anomalous depends upon which materials water is to be compared and
the interpretation of 'anomalous'. For example, it could well be argued
that water possesses exactly those properties that one might deduce from
its structure (see for example, [402]). Other
tetrahedrally interacting liquids, such as liquid Si, SiO2 and
BeF2 have many similar 'anomalies'. Comparisons between water,
liquid sodium, argon and benzene appear to Franks [112]
to indicate several of the properties given above as not being anomalous.
However, these materials are perhaps not the most typical of liquids. My
list gives the unusual properties generally understood to make liquid
water (and ice) stand out from 'typical' liquids (or solids). See [242]
for a review concentrating on the non-anomalous properties of water; that
is, those that are the 'same' as for other liquids. [Back]

b It is therefore very difficult to obtain really
pure water (for example, < 5 ng g-1). For a review of aqueous
solubility prediction, see [744]. Note that
ice, in contrast, is a very poor solvent and this may be made use of when
purifying water (for example, degassing) using successive freeze-thaw
cycles. [Back]

c Some scientists attribute the low temperature
anomalous nature of water to the presence of a
second critical point; an interesting if somewhat unproductive
hypothesis as a sole explanation (as the attribution mixes cause with
effect). Water's anomalies do not require this as an explanation. [Back]

d The temperature range of 'hot' and 'cold' water
varies in these examples; see the individual entries for details. [Back]

e The anomalies of water are divided into groups
but, clearly, some anomalies may be included under more than one topic and
there may not be universal agreement for the groupings shown. [Back]

P1 High melting point (0°C, compare
CHCl3 -63°C)

The melting point of water is over 100 K higher than
expected by extrapolation of the
melting points of other Group 6A
hydrides, here above shown compared with
Group 4A hydrides. It is also much higher than O2
(54 K) or H2 (4 K). See also
below for further comparisons.

In ice (Ih), all water molecules
participate in four hydrogen bonds (two as donor and two as acceptor) and
are held relatively static. In liquid water, some of the weaker hydrogen
bonds must be broken to allow the molecules to move around. The large
energy required for breaking these bonds must be supplied during the
melting process and only a relatively minor amount of energy is reclaimed
from the change in volume (PΔV = -0.166 J mol-1). The free
energy change (ΔG=ΔH-TΔS, where ΔH=ΔU+PΔV) must be zero at the melting
point. As temperature is increased, the amount of hydrogen bonding in
liquid water decreases and its entropy increases. Melting will only occur
when there is sufficient entropy change to provide the energy required for
the bond breaking. The low entropy (high organization) of liquid water
causes this melting point to be high.

Although ice is very difficult to superheat above its (equilibrium)
melting point, tiny amounts of
ice (Ih) have been superheated to 290 K
(without melting) for very short periods (>250 ps) [954a]
with the limit of superheating (>1 ns) established at about 330 K [954b].
[Back]

P2 High boiling point (100°C, compare
CHCl3 61°C)

The boiling point of water is over 150 K higher than
expected by extrapolation of the boiling
points of other Group 6A hydrides, here
shown compared with Group 4A hydrides. It
is also much higher than O2 (90 K) or H2 (20 K).
See also below for further comparisons.

There is considerable hydrogen bonding in liquid water
resulting in high cohesion (water's cohesive
energy density is 2.6 times that of methanol), which prevents
water molecules from being easily released from the water's surface.
Consequentially, the vapor pressure is reduced. As boiling cannot
occur until this vapor pressure equals the external pressure, a higher
temperature is required.

The pressure/temperature range of liquidity
for water is much larger than for most other materials (for example, under
ambient pressure the liquid range of water is 100°C whereas for both H2S
and H2Se it is about 25°C. [Back]

P3 High critical point (374°C, compare
CH3CH3 32°C)

The critical point of water
is over 250 K higher than expected by
extrapolation of the critical points of other
Group 6A hydrides, here shown compared
with Group 4A hydrides. For example, the
critical point (647 K, 22.06 MPa 322 kg m-3) is far higher
than ethanol (514 K, 6.14 MPa 276 kg m-3), which also
hydrogen bonds (but in chains not 3-dimensional) and is much larger
and more massive.

The critical point can only be reached when the
interactions between the water molecules fall below a certain
threshold level. Due to the strength and extent of the hydrogen
bonding, much energy is needed to cause this reduction in molecular
interaction and this requires higher temperatures. Even close to the
critical point, a considerable number of hydrogen bonds remain, albeit
bent, elongated and no longer tetrahedrally arranged [92].

The critical points (C.Pt.), boiling points (B.Pt.)
and melting points (M.Pt.) of the molecules isoelectronic with water
shows water to have higher values.

Ammonia and hydrogen fluoride also have somewhat raised values as
they form molecular clustering, albeit with three donor H-atoms and
one lone pair acceptor group or one donor H-atom and three lone pair
acceptor groups, respectively; giving a maximum of two hydrogen bonds
per molecule, on average. Although solid HF forms stronger hydrogen
bonds, these form linear zigzag chains with no rings or polygons and
hence its three-dimensional structure is weaker. The hydrogen bonds in
solid NH3 can form three-dimensional arrangements but are
distorted and weakened. Water has two donor H-atoms and two lone pair
acceptor groups with close to tetrahedral angles giving the
possibility of four hydrogen bonds per molecule with little
distortion. [Back]

P4 Solid water exists in a wider
variety of stable (and metastable) crystal and amorphous structures than
other materials.

The ability for water to form extensive networks of hydrogen bonds
increases the number of solid phases
possible. The open structure of hexagonal ice
(19.65 cm3 mol-1), which contains only about 7.5 cm3
mol-1 of water molecules, gives plenty of scope for different
arrangements of the water molecules as the structure is compressed. For
comparison, hydrogen sulfide has only four distinct solid phases [119].
[Back]

P5 The thermal conductivity of ice reduces with increasing pressure

Hexagonal ice shows anomalous reduction in thermal conductivity with
increasing pressure (as do cubic ice and
low-density amorphous ice but not
high-density amorphous ice ), which behavior
is different from most crystals where thermal conductivity increases with
increasing density. Low-density amorphous ice is the only glass to show
this peculiar behavior. This anomaly is due to the pressure-induced
bending of the hydrogen bonding decreasing the transverse sound velocity [617].
[Back]

P6 The structure of liquid water changes at high pressure

In a similar manner to the formation of the high density crystalline (ice-five
and ice seven) and amorphous (HDA)
ice phases, it is likely that liquid water undergoes a significant change
in structure at high pressure (about 200 MPa for liquid water). The
pressure-viscosity,
self-diffusion, compressibility and
structural properties of water change above
about 200 MPa. Other changes also occur around 200 MPa, such as the loss
of the density maximum and the discontinuity
in fast sound in liquid water. The
explanation for all these effects is that there appears to be an increase
in interpenetration of hydrogen bonded networks at about 200 MPa (at 290
K); interpenetration of hydrogen bonded clusters being preferred over more
extreme bending or breaking of the hydrogen bonds. This structuring for
liquid water at high pressures is consistent to that found by neutron
scattering [1001] and indicates that liquid
water structuring at high pressure has similarity to that of its high
pressure ice phases [1254]. [Back]

P7 Supercooled water has two phases and a
second critical point

As water is supercooled it converts mainly into its expanded form (for
example, ES) at ambient pressures, which at
low enough temperatures (< -38°C) may result in it forming metastable
low-density amorphous ice (LDA; although
normally it will form hexagonal ice at this
temperature). If the pressure on LDA is increased above about 200 MPa then
LDA undergoes a 30% collapse forming metastable high-density amorphous ice
(HDA) but notably in a continuous process
without breaking the hydrogen bonds [394].
This phase change cannot continue to higher
temperatures (so creating a second critical point,
[45]) as neither of these phases is stable in
the presence of liquid water although they may convert into their
metastable supercooled liquid forms. The presence of these low- and
higher-density forms of liquid (supercooled) water leads to the
breakdown of the Stokes-Einstein relationship
in supercooled water [1040] occurring far
above the glass-transition temperature, in
contrast to many supercooled liquids where this behavior is found only at
temperatures just above this transition [1040b].
[Back]

P8 Liquid water is easily supercooled but glassified with difficulty

Water freezing is not simply the reverse of ice melting [1110].
Melting is a single step process that ocurrs at the melting point as ice
is heated whereas freezing of liquid water on cooling involves
ice crystal nucleation and crystal growth
that generally is initiated a few degrees below the melting point even for
pure water. Liquid water below its melting point is supercooled water. It
may be expected that the directional hydrogen bonding capacity of water
would reduce its tendency to supercool as it would encourage the regular
structuring in cold liquid that may lead to a crystalline state. Liquid
water, however, is easily supercooled down to about -25°C and with more
difficulty down to about -38°C with further supercooling possible, in tiny
droplets (~5 μm diameter), down to about -41°C under normal atmospheric
pressure. Water, supercooled down to -37.5°C, is sustained in storm clouds
and the condensed clouds formed by aircraft at high altitude. Rather
strangely, at the limit of this supercooling (also known as the
homogeneous freezing point) the water activity
is always 0.305 lower than that of water melting at the same temperature [457].
Where salts or hydrophilic solutes are present, the homogeneous freezing
point reduces about twice as much as the melting point [663].

Liquid water may be maximally supercooled to about -92°C and 210 MPa.
It should be noted that bulk water never forms a glass as the glass
transition temperature (Tg, = ~136 K) for water is far
lower, relative to its melting point (Tm, 273 K), than
expected; Tm/Tg ~ 2 rather than
Tm/Tg ~ 1.3-1.5 as for more
typical liquids. Thus supercooled bulk water (i.e. not affected
by surfaces or solutes) always crystallizes before its temperature can be
sufficiently lowered, whatever the cooling rate [558].
Water glass may only be produced by extremely
rapid cooling (105 K s-1) of tiny volumes of water
(<~100 μm diameter).

As water is cooled, the cluster equilibrium
shifts towards the more open structure (e.g. ES ) with higher viscosity. In
order for crystallization to occur at least 3 - 4 unit cells worth of
water molecules have to come together in the correct orientation.b
The formation of whole or part icosahedral clusters interferes with this
process whilst not allowing cluster crystallization due to their five fold
symmetry. Lowering the temperature further, which should encourage
crystallization, is partially counteracted by the increase in icosahedral
clustering. The presence of
ES clusters is, in principle, in
agreement with computer simulation studies requiring the presence of
metastable states [216]. Methods that break
the hydrogen bonding in these clusters, such as ultrasonics [296],
cause the supercooled water to immediately freeze.

There is a recent comprehensive review of the properties of supercooled
water [569]. [Back]

P9 Liquid water exists at very low temperatures and freezes on
heating

Deeply supercooled liquid water can be
produced from glassy amorphous ice between
-123°C and - 149°C [74] and may coexist with
cubic ice up to -63°C [137]. This behavior is
particularly anomalous as the liquid (deeply supercooled water) is a 'strong'
liquid (compared with supercooled water that is a 'fragile'
liquid [493]) that changes to crystalline
solid (cubic ice) on increasing the
temperature whilst keeping the pressure constant. Deeply supercooled water
exists in the liquid state where it appears to be too cold to diffuse
sufficiently quickly to crystallize noticeably. A possible explanation of
this low-temperature-range liquid water may be the formation of
strands of icosahedral structures. This model
can also explain the high viscosity and strong
(that is, low specific heat) liquid behavior of this extremely supercooled
water [215]. The unusual behavior of this
liquid (that is, deeply supercooled water), by solidifying on heating, has
been found with other liquids (for example, methyl
cellulose and some cyclodextrin solutions [1026]).
[Back]

P10 Liquid water may be easily superheated

Liquid water can be easily superheated above its boiling point away
from its surface with the atmosphere [1128,
1184]. This may be particularly important
when heating foods and drinks in a microwave oven where explosive
production of steam from the superheated water may cause severe injuries.
Superheating is also causes the boiling point of water to vary, in much
the same way as its freezing point, and of
irregular boiling, that is, 'bumping' [1184].
Liquid water may be superheated to about +240°C to +280°C in capillaries
or small droplets within high-boiling immiscible solvents. Superheating is
also apparent at low tepertures but at negative pressures (i.e. stretched
water). Water may be superheated by reducing the pressure to below -100
MPa at 20°C [1128]. Superheating is
facilitated by dissolved gas that may increase its hydrogen-bonded order [821]
but prevented by the presence of gas bubbles or
nanobubbles (that is, cavities) that act as initiation sites for
vaporization.

Water vapor (gas) may easily be cooled below its condensation
temperature (dew point) for its partial pressure (i.e. its
boiling point ) in the absence of dust, or other, particles or surfaces
that help the nucleation process [1184].

An interesting, if unrelated effect (the Leidenfrost effect), is that
water droplets remain far longer on a hotplate just above 200°C than if
the hotplate was just above 100°C. (see [960]
for an amusing scientific answer to how water boils). [Back]

P11 Hot water may freeze faster than cold water; the Mpemba effect

The ability of hot water to freeze faster than cold seems
counter-intuitive as it would seem that hot water must first become cold
water and therefore the time required for this will always delay its
freezing relative to cold water. However experiments show that hot water
(for example, 90 °C) does often (but by no means always) appear to freeze
faster than the same amount of cold water (for example, 18°C) under
otherwise identical conditions [158]. This
has been recognized even as far back as Aristotle in the 4th
century BC but was brought to the attention of the scientific community by
the perseverance of Erasto Mpemba a schoolboy at Iringa School, Tanzania,
who refused to reject his own evidence, or bow to disbelieving mockery,
that he could freeze ice cream faster if he warmed it first. For a recent
review of the Mpemba effect, see [959].

A number of explanations have been put
forward but the most likely scenario (described in [158])
is that the degree of supercooling is greater, under some
circumstances, in initially-cold water than initially-hot water. The
initially-hot water appears to freeze at a higher temperature (less
supercooling) but less of the apparently frozen ice is solid and a
considerable amount is trapped liquid water. Initially-cold water
freezes at a lower temperature to a more completely solid ice with
less included liquid water; the lower temperature causing intensive
nucleation and a faster crystal growth rate. If the freezing
temperature is kept about -6°C then the initially-hot water is most
likely to (apparently) freeze first. If freezing is continued,
initially-cold water always completely freezes before initially-hot
water.

Why initially-cold water supercools more is explained in terms of the
gas concentration and the clustering of water. Icosahedral clusters do not
readily allow the necessary arrangement of water molecules to enable
hexagonal ice crystal initiation; such clustering is the cause of the
facile supercooling of water. Water that is
initially-cold will have the maximum (equilibrium) concentration of such
icosahedral clustering. Initially-hot water has lost much of its ordered
clustering and, if the cooling time is sufficiently short, this will not
be fully re-attained before freezing. Experiments on low-density water
around macromolecules have shown that such clustering processes may take
some time [4]. It is also possible that
dissolved gases may encourage supercooling by (1) increasing the degree of
structuring, by hydrophobic hydration, in the previously-cold water
relative to the gas-reduced previously-hot water (the critical effect of
low concentrations of dissolved gas on water structure is reported in [294];
re-equilibration taking several days) and (2) increasing the pressure as
gas comes out of solution when the water starts to crystallize, so
lowering the melting point and reducing the tendency to freeze (see
guestbook). Also, the presence of tiny gas bubbles (cavities
produced on heating) may increase the rate of nucleation, so reducing
supercooling [428]. Recently another
possibility has been described depending on changes in dissolved material
with temperature (such as the reduction in bicarbonate in heated 'hard'
water), but this has not yet been experimentally tested [1014].
The rationale for the Mpemba effect in this case concerns differences in
the solute concentration at the ice-liquid interface causing a localized
lowering of the melting point [1014].
[Back]

P12 Warm water vibrates longer than cold water

It is expected that the lifetime of an excited molecular vibration
should decrease as the temperature increases as the energy and likelihood
of interactions with other molecules also both increase. For example, the
lifetime of the excited liquid HCl stretch vibration decreases from 2.1 ns
at 173 K to 1.0 ns at 248 K.

In liquid water, the excited OH-stretch vibration has a lifetime of
0.26 ps at 298 K and this lifetime increases to 0.32 ps at 358 K [592].
The reason for this is due to the effects of the hydrogen-bonded network.
The OH-stretch vibration normally relaxes by transferring energy to an
overtone of the H-O-H bending vibration. However, as the temperature
increases the hydrogen bonds of water get weaker, which leads to an
increase of the frequency of the stretch vibration and a decrease of the
frequency of the bending vibration. As a result, the overtone of the
bending mode shifts out of resonance with the stretching mode, thereby
making the energy transfer less likely. [Back]

Footnotes

a The surface temperature on Mars lies below the triple
point of water and its atmospheric pressure is close to this value, such
that no liquid water may be found there. [Back]

b Theoretical considerations concerning the ice
nucleation site size gives estimates of 45,000 water molecules at -5°C
down to 70 water molecules at -40°C [265].
Molecular dynamics studies show that these do not need to form a
crystalline structure for crystallization to occur [347].
[Back]

Water structure and science
(http://www.lsbu.ac.uk/water/explan2.html)

Explanation of the Density
Anomalies of Water (D1-D20)

D1 The density of ice increases on heating (up to 70 K)

Most solids expand and become less dense when heated.
Hexagonal, cubic
and amorphous ices all become denser at low
temperatures. All expand slightly with cooling at all temperatures below
about 70 K with a minimum thermal expansivity at about 33 K (expansion
coefficient (α) ~ -0.000003 K-1). This appears to be due to
alteration in the net bending motion of three tetrahedral
hydrogen bonded molecules with temperature,
as higher frequency modes are reduced [209].
This is a similar but unrelated phenomenon to the
maximum density anomaly that occurs in liquid water. [Back]

It is usual for liquids to contract on freezing and expand on
melting. This is because the molecules are in fixed positions within
the solid but require more space to move around within the liquid.

When water freezes at 0°C its volume increases
by about 9% under atmospheric pressure. If the melting point is
lowered by increased pressure, the increase in volume on freezing is
even greater (for example, 16.8% at -20°C [561]).
Opposite is shown the molar volumes of ice and water along the melting
point curve [561].

The structure of ice (Ih) is open with a
low packing efficiency where all the water molecules are involved in four
straight tetrahedrally-oriented hydrogen bonds; for comparison, solid
hydrogen sulfide has a face centered cubic closed packed structure with
each molecule having twelve nearest neighbors [119].
On melting, some of these ice (Ih) bonds
break, others bend and the structure undergoes a partial collapse, like
other tetrahedrally arranged solids such as the silica responsible for the
Earth's crust floating on the outside of our planet. This is different
from what happens with most solids, where the extra movement available in
the liquid phase requires more space and therefore melting is accompanied
by expansion.

In contrast, it should be noted that the high-pressure ices (ice
III, ice
V, ice
VI and ice
VII) all expand
on melting to form liquid water (under high pressure). It is the
expansion in volume when going from liquid to solid, under ambient
pressure, that causes much of the tissue damage in biological organisms on
freezing. In contrast, freezing under high pressure directly to the more
dense ice VI may
cause little structural damage [535].

An interesting phenomenon, due to the expansion on freezing, is the
formation of thin ice spikes that
occasionally grow out of (pure water) ice cubes on freezing [564a].
This phenomenon appears to be a general property of any material that
expands on freezing [564b]. [Back]

Increasing pressure normally promotes liquid freezing, shifting
the melting point to higher temperatures. This is shown by a forward
sloping liquid/solid line in the phase diagram. In water,
this line is backward sloping with slope
13 MPa K-1 at 0°C, 101.325 kPa. As the pressure increases,
the liquid water equilibrium shifts
towards a collapsed structure (for example,
CS ) with higher entropy. This
lowers the melting free energy change (ΔG=ΔH-TΔS) such that it will be
zero (that is, at the melting point) at a lower temperature.

The minimum temperature that liquid water can exist without ever
freezing is -21.985°C at 209.9 MPa; at higher pressures water freezes
to ice-three,
ice-five, ice-six or
ice-seven at increasing temperatures.
Stretching ice has the reverse effect;
ice melting at +6.5°C at about -95 MPa negative pressure within
stretched microscopic aqueous pockets in mineral fluorite [243].a

It should be noted that ice skating (or skiing) does not produce
sufficient pressure to lower the melting point significantly, except
at very sharp edges, or involving powdered ice on the ice surface. The
increase in slipperiness is normally generated by frictional heating,
perhaps initially involving the ultra-thin
surface layer of disorganized and weakly held frozen water (see
[1238] for a review).

If the increase in volume on freezing is prevented, an increased
pressure of up to 25 MPa may be generated in water pipes; easily capable
of bursting them in Winterb. An
interesting question concerns what would happen to water cooled below 0°C
within a vessel that cannot change its volume (isochoric cooling). Clearly
if ice forms, its increased volume causes an increase in pressure which
would lower the freezing point at least until the lowest melting point
(-21.985°C) is reached at 209.9 MPa.e
A recent thermodynamic analysis concludes that ice nucleation cannot arise
above -109°C during isochoric cooling [1053],
which is close to the upper bound of the realm of deeply supercooled water
(-113°C), so it is unclear if ice would ever freeze in such a (unreal)
system. [Back]

Melting ice, within a filled and sealed fixed volume, may result in an
apparently superheated state where the metastable iso-dense liquid water
is stretched, relative to its equilibrium state at the (effectively)
negative pressure, due to its cohesiveness. Consequently, the
ESCS
equilibrium is shifted towards the more-open
ES structure. [Back]

D4 Liquid water has a high density that increases on heating (up to
3.984°C)

The high density of liquid water is due mainly to the cohesive nature
of the hydrogen-bonded network, with each water molecule capable of
forming four hydrogen bonds.g This
reduces the free volume and ensures a relatively high-density, partially
compensating for the open nature of the hydrogen-bonded network. Its
density, however, is not as great as that of closely packed, isoelectronic,
liquid neon (1207 kg m-3 at 27 K, with molar volume 92.8% of
water). It is usual for liquids to expand when heated, at all
temperatures. The change in density is almost mirrored by the size of
ortho-positronium bubbles,c which
are affected by the free volume available and show a minimum at 8°C [826].The
anomalous temperature-density behavior of water can be explained as
previously [13, 14,
1354] utilizing the range of environments
within whole or partially formed clusters with differing degrees of
dodecahedral puckering. The density maximum (and molar volume minimum) is
brought about by the opposing effects of increasing temperature, causing
both structural collapse that increases density and thermal expansion that
lowers density. At lower temperatures there is a higher concentration of
ES whereas at higher temperatures
there is more
CS and fragments, but the volume
they occupy expands with temperature. The change from
ES to
CS as the temperature rises is
accompanied by positive changes in both entropy and enthalpy due to the
less ordered structure and greater hydrogen bond bending respectively.

The change in density with temperature causes an inversion in cold
water systems as the temperature is raised above about 4°C. Thus in water
below about 4°C, warmer water sinks whereas when above about 4°C, warmer
water rises. As water warms up or cools down through 4°C, this process
causes considerable mixing with useful consequences such as increased gas
exchange.

Shown below is the variation of the
density of ice, liquid
water, supercooled water and
water vapor, in equilibrium with the liquid,
with temperature (the orthobaric density).

The diagram helps explain why liquid water cannot exist above the
critical point (C.Pt.). Also shown (inset) is the variation of the
molar volume of liquid water with temperature about the density
maximum (at 3.984°C). Note the unusual and rapid approach of the
densities of supercooled water and ice (estimated at -50°C, 100 kPa [580])
at about the homogeneous nucleation temperature (~-45°C, 101 kPa).
This approach moves to lower temperatures at higher pressures,
seemingly absent at ~200 MPa [561] (see
below, D5). [Back]

The occurrence of a density maximum, as in water, is
sometimes if only rarely found (or predicted) in other liquids , such
as He, Te, Si and SiO2 for a variety of reasons. The effect
in liquid He4 is thought due to zero point energy and a
similar reason has been put forward for water [1301]
although, in practical terms, this presents a related if alternative
approach to that above.

Inversely related to changes in densities are the changes in
volumes. Opposite are shown pressure-temperature curves of liquid
water at constant volume; showing the change in pressure that would
occur with temperature using a (theoretically ideal) constant volume
container. There is a minimum in the curve only for volumes greater
than 0.986 cm3 g-1. The data were obtained from
the IAPWS-95 equations [540].

D5 Increased pressure reduces the temperature of maximum density

Increasing pressure shifts the water equilibrium
towards a more collapsed structure (for example,
CS). So, although pressure will
increase the density of water at all temperatures (flattening the
temperature density curve), there will be a disproportionate effect at
lower temperatures. The result is a shift in the temperature of maximum
density to lower temperatures. At high enough pressures the density
maximum is shifted to below 0°C (at just over 18.84 MPa). Above 28.33 MPa
it cannot be observed above the melting point (now at 270.97 K) and it
cannot be observed at all above about 200 MPa. A similar effect may be
caused by increasing salt concentration, which behaves like
increased pressure in breaking up the
low-density clusters. Thus in 0.36 molal NaCl the temperature of freezing
and maximum density coincide at -1.33°C. Higher salt concentrations reduce
the temperature of maximum density such that it is only accessible in the
supercooled liquid. Lowering the temperature of maximum density is not a
colligative property as both the nature and concentration of the soluted
affects the degree of lowering. The stronger and more linear
hydrogen bonding in D2O gives rise
to a 25% smaller shift in the temperature of maximum density (from
11.185°C at 0.1 MPa) with respect to increasing pressure [726].

Under negative pressure (that is, increased stretching of liquid water)
the temperature of maximum density increases. However, the temperature of
maximum density shows a maximum with respect to pressure in this negative
pressure region [419], as at very high
negative pressures it reduces as the hydrogen bonds are stretched to
breaking point; [Back]

D6 There is a minimum in the density of supercooled water

At a temperature below the maximum density
anomaly there must be a minimum density anomaly so long as no phase
change occurs, as the density increases with reducing temperature at much
lower temperatures. This was first seen in simulations [498]
and is expected to lie below the minimum temperature accessible on
supercooling (232 K, [215]) and close to
where both maximum
ES structuring and
compressibility occur, with the liquid
density close to that of hexagonal ice
(latterly confirmed [871]). It is evident
that most anomalous behavior must involve a quite sudden discontinuity at
about the homogeneous nucleation temperature (~228 K, where the densities
of supercooled water and ice approach) as the tetrahedrally arranged
hydrogen bonding approaches its limit (two acceptor and two donor hydrogen
bonds per water molecule) and no further density reduction is possible
without an energetically unfavorable stretching (or breaking) of the
bonds. By use of optical scattering data of confined water and a model
that divides the liquid water into two forms of low and high density, the
density minimum has been proposed to lie at 203±5 K [1325].
A density minimum at 210 K has been experimentally determined in
supercooled D2O contained in 1-D cylindrical pores of
mesoporous silica [1195]. Although possibly
related, density values obtained for confined water cannot be taken as
necessarily giving the density minimum for the bulk supercooled liquid
however. [Back]

D7 Water has a low thermal expansivity (0.00021/°C, cf. CCl4
0.00124/°C at 20°C)

The thermal expansivity is zero at 3.984°C, being negative below and
positive above (see density and
expansivity anomalies). As the temperature
increases above 3.984°C, the cluster equilibrium
shifts towards the more collapsed structure (for example,
CS), which reduces any increase in
volume due to the increased kinetic energy of the molecules. Normally the
higher the volume a molecule occupies, the larger is the disorder
(entropy). Thermal expansivity (αP)
αP = [δV/δT]P/V
<(δV)(δS)>TPN
depends on the product of the fluctuations in these factors. In water,
however, the more open structure (for example,
ES) is also more ordered (that is,
as the volume of liquid water increases on lowering the temperature below
3.984°C, the entropy of liquid water reduces). [Back]

It is usual for liquids to expand increasingly with increased
temperature.

Supercooled and cold (< 3.984°C) liquid water both
contract on heating [68].
As the temperature decreases, the cluster
equilibrium shifts towards the expanded, more open, structure
(for example,
ES), which more than
compensates for any decrease in volume due to the reduction in the
kinetic energy of the molecules. It should be noted that this behavior
requires that the thermodynamic work (dW) equals -pΔV rather than the
usual +pΔV (pressure times change in volume) [404].
The behavior expected, if water acted as most other liquids at lower
temperatures, is shown as the dashed line opposite. The blue line
shows the expansivity of ice. Also, for water and other materials with
negative thermal expansivity, both
and
are negative [1147] whereas normally both
are positive.

D9 Water's thermal expansivity increases with increased pressure.

The thermal expansion of water increases with
increased pressure up to about 44°C in contrast to most other liquids
where thermal expansion decreases with increased pressure. This is due
to the collapsed structure of water having a greater thermal
expansivity than the expanded structure and the increasing pressure
shifting the equilibrium towards a more collapsed structure.

Opposite is shown (blue area) the range of
temperatures and pressures where the thermal expansion increases with
increased pressure. [Back]

D10 The number of nearest neighbors increases on melting

Each water molecule in hexagonal ice has
four nearest neighbors. On melting, the partial collapse of the open
hydrogen bonded network allows nonbonded molecules to approach more
closely so increasing this number. Normally in a liquid the movement of
molecules, and the extra space they find themselves in, means that it
becomes less likely that they will be found close to each other; for
example, argon has exactly twelve nearest neighbors in the solid state but
only an average of about ten on melting. [Back]

D11 Nearest neighbors increase with temperature

If a water molecule is in a fully hydrogen-bonded structure with strong
and straight hydrogen bonds (such as hexagonal ice)
then it will only have four nearest neighbors. In the liquid phase,
molecules approach more closely due to the partial collapse of the open
hydrogen bonded network. As the temperature of liquid water increases, the
continuing collapse of the hydrogen bonded network allows nonbonded
molecules to approach more closely so increasing the number of nearest
neighbors. This is in contrast to normal liquids where the increasing
kinetic energy of molecules and space available due to expansion, as the
temperature is raised, means that it becomes less likely that molecules
will be found close to each other. [Back]

It may be thought that water should have a high compressibility (κT
= -[δV/δP]T/V) as the large cavities
in liquid water allows plenty of scope for the water structure to collapse
under pressure without water molecules approaching close enough to repel
each other. The deformation causes the growth in the radial distribution
function peak at about 3.5 Å with increasing or pressure [51]
(and temperature [50]), due to the collapsing
structure. The low compressibility of water is due to water's
high-density, again due to the cohesive nature of the extensive hydrogen
bonding. This reduces the free space (compared with other liquids) to a
greater extent than the contained cavities increase it. At low
temperatures D2O has a higher compressibility than H2O
(for example, 4% higher at 10°C but only 2% higher at 40°C [188])
due its stronger hydrogen bonding producing
an ESCS
equilibrium shifted towards the more-open
ES structure. Also noteworthy is
that solutions of highly compressible liquids, such as diethyl ether (1.88
GPa-1) in water, reduce the compressibility of the water, as
they occupy its clathrate cavities. [Back]

D13 Compressibility drops as temperature increases (up to a minimum
at about 46.5°C)

In a typical liquid the compressibility decreases as the structure
becomes more compact due to lowered temperature. In water, the cluster
equilibrium shifts towards the more open
structure (for example,
ES ) as the temperature is reduced
due to it favoring the more ordered structure (that is, ΔG for
ESCS
becomes more positive). As the water structure is more open at these lower
temperatures, the capacity for it to be compressed increases [68].

The effect is not a simple dependency on density, however, or else
the minimum at 46.5°C for isothermal (that is, without change in
temperature) compressibility
κT = -[δV/δP]T/V
κT = [δρ/δP]T/ρ <(δV)2>TPN
and the minimum at 64°C for adiabatic (that is, without loss or gain
of heat energy, also called isentropic) compressibility (κS
= -[δV/δP]S/V [112]) would
both be at the density minimum (4°C). Relationships between κT
and κS are given elsewhere.

The adiabatic compressibility lies below the isothermal
compressibility except at the temperature of
maximum density where they are equal.

Compressibility depends on fluctuations in the specific volume and
these will be large where water molecules fluctuate between being
associated with a more open structure, or not, and between the different
environments within the water clusters. At high pressures (for example,
~200 MPa) this compressibility anomaly, although still present, is far
less apparent [706].

Some other liquids, such as formamide (also extensively hydrogen
bonded), show a compressibility minimum. [Back]

D14 There is a maximum in the compressibility-temperature
relationship

At sufficiently low temperature, there must be a maximum in this
compressibility-temperature relationship, so long as no phase change
occurs, as the compressibility decreases with reducing temperature at much
lower temperatures.. This is expected to lie just below the minimum
temperature accessible on supercooling (232 K, [215])
close to the temperature of minimum density.
[Back]

D15 Speed of sound is slow and increases with temperature (up to a
maximum at 74°C)

Sound is a longitudinal pressure wave, whereby the energy is propagated
as deformations in the media but the molecules then return to their
original positions and are not propagated. The propagation of a sound wave
depends on the transfer of vibration from one molecule to another. In a
typical liquid, the speed of sound is faster (see fast sound) and
decreases as the temperature increases, at all temperatures. The speed of
sound in water is almost five times greater than that in air (340 m s-1).

The speed (u) is given by u2 = 1/κSρ = [δP/δρ]S
~ 1/(<(¶V)2>) [802] where κS is
the adiabatic compressibility, ρ is the density and P the pressure. The
anomalous nature of both these physical properties is described above (compressibility,
density).

At low temperatures both compressibility and density are high, so
causing a lower speed of sound. As the temperature increases the
compressibility drops and goes through a minimum whereas the density
goes through a maximum and then drops [67].
Combination of these two properties leads to the maximum in the speed
of sound. Increasing the pressure increases the speed of sound and
shifts the maximum to higher temperatures, both in line with the
effect on the density. The supercooled data has been
calculated for the graph, right.

The presence of salt causes small shifts in the temperature maximum in
line with the Hofmeister series; reducing the
temperature at higher concentrations. Ionic
kosmotropes cause a slight increase in the temperature maximum at
low concentrations [921]. [Back]

D16 The speed of sound may show a minimum

Depending on the frequency, there may be a minimum in the speed of
sound at low temperatures [568]. Although
this may be thought due to compensation in the changes in density
decrease and compressibility increase with lowering temperature, this
is not apparent in the calculated dataabove. It is most likely due to the
increasing strength of its hydrogen bonding and consequential
transition to 'fast sound' at lower frequencies (see
below). The data opposite is from [1151]

The speed of sound in the oceans has a minimum at about 1000 m where
the increase in speed due to increasing pressure balances the
decreasing speed with drop in temperature. Sound waves are trapped and
propagate horizontally in this
SOFAR channel. [Back]

D17 'Fast sound' is found at high frequencies and shows an
discontinuity at higher pressure

Water has a second sound 'anomaly' (called 'fast sound') concerning the
speed of sound. Over a range of high frequencies (> 4 nm-1)
liquid water behaves as though it is a glassy solid rather than a liquid
and sound travels at about twice its normal speed (~3200 m s-1;
similar to the speed of sound in ice 1h). There is little effect of
temperature below 20°C [1151]. At lower
temperatures the speed of sound increases from its low frequency value
towards the high frequency value (i.e. 'fast sound') at lower frequencies,
giving rise to a minimum in the temperature-speed of sound relationship [1151]
(see above). 'Fast sound' is not a true
anomaly as this behavior is what might be expected from a typical liquid,
whereas the (hydrodynamic) lower speed of sound
(~1500 m s-1) is due to the hydrogen bonding network structure
of water. However, there does appear to be a discontinuity anomaly at a
density of about 1.12 g cm-1 (in this 'fast sound' only; the
discontinuity is less apparent in the hydrodynamic speed of sound) that
may indicate a structural rearrangement [644,
655], due to the gradual phase transition to
interpenetrating hydrogen bonded networks at the higher pressures, as seen
with other anomalies. [Back]

D18 NMR spin-lattice relaxation time is very small at low
temperatures

NMR spin-lattice relaxation time depends on the degree of structure. As
the water cluster equilibrium shifts towards
a stiffer, tetrahedrally organized, structure (for example,
ES) as the temperature is lowered,
the NMR spin-lattice relaxation time reduces far more than would otherwise
be expected [53a]. This effect can be
partially reversed by increasing the pressure, which reduces the degree of
structure. [Back]

D19 The refractive index of water has a maximum value at just below
0°C.

The refractive index of water (λ = 589.26 nm) rises from an
estimated 1.33026 at -30°C to a maximum value at just below 0°C
(1.33434) before falling ever increasingly to 1.31854 at 100°C [310].
This may be explained by the mixture model [60]
applied to the change from
ES to
CS as the temperature rises;
ES possessing a lower
refractive index than
CS. Most of the effect is due
to the density difference between
ES and
CS. Higher density produces
higher refractive index such that the refractive index temperature
maximum lies close to the density maximum, with the small difference
due to the slightly different effect of temperature on the specific
refractions of
ES and
CS. Although not considered
anomalous, it is interesting to note that ice has the lowest
refractive index (1.31, λ = 589 nm) of any known crystal. [Back]

D20 The change in volume as liquid changes to gas is very large.

Water is one of the lightest gasses but forms a
dense liquid. The volume change is the greatest known (except for
metals) at 1603.6 fold, at the boiling point and standard atmospheric
pressure. This change in volume allows water to be of great use in the
steam generation of electrical power. [Back]

Footnotes

a There is some dispute over whether such a negative
pressure can be reached [917]. [Back]

b Pipes burst due to the rapid formation of a network
of feathery dendritic ice enclosing water which then expands on freezing
within a now restricted volume to generate the required pressure [354].
The curious phenomenon of hot water pipes bursting more often than cold
water pipes (see [959]) is due to the
differences in this dendritic ice formation causing blockage in the pipes
at low percentage ice formation. [Back]

cortho-Positronium consists of a positron -
electron pair with parallel spins [826],
created here by positron irradiation of water. [Back]

d The depression in the temperature of maximum density is
linearly related to concentration for most solutes (ethanol and methanol
are exceptional giving a slight increase in the temperature of maximum
density at low concentrations) [1037], as
discovered in 1839 by Despretz. [Back]

e It would be impossible to reach this pressure in a
container, unless pressure was also exerted from the outside, due to the
pressure induced expansion of the vessel. [Back]

f Others take a contrary view, stating that water's
compressibility is twice that expected [53b].
This difference is down to the viewpoint and different theoretical
expectations. In both cases, water's compressibility is unexpected; either
being greater than expected due to water's open structure or less than
expected (in spite of its open structure) due to the cohesive nature of
its extensive hydrogen bonding. [Back]

g In liquid methanol (CH3OH) the oxygen atoms are
3% closer than they are in liquid water but its density is 21% less than
water, due to methanol only able to form only two hydrogen bonds per
molecule. [Back]

Water structure and science
(http://www.lsbu.ac.uk/water/explan4.html)

Explanation of the Thermodynamic
Anomalies of Water (T1-T11)

T1 The heat of fusion of water with temperature exhibits a maximum
at -17°C [15].

This strange behavior has been determined from the variation in ice and
water specific heat capacities (Cp). It is due to changes in
the structuring of supercooled water. As the temperature is lowered from
0°C the hydrogen-bond strength of ice increases due to the reduction in
their vibrational energy and this gives rise to an increasing difference
(as temperature is lowered) between the enthalpy of the water and ice. At
low temperatures (below about -17°C) the continued shift, with lowering
temperature, in the supercooled water
CSES
equilibrium towards the
ES structure reduces the enthalpy
of the liquid water relative to the ice due to the consequent increase in
hydrogen-bond strength and this causes the drop in the heat of fusion with
lowering temperature. [Back]

Water has the highest specific heat of all liquids except ammonia. As
water is heated, the increased movement of water causes the hydrogen bonds
to bend and break. As the energy absorbed in these processes is not
available to increase the kinetic energy of the water, it takes
considerable heat to raise water's temperature. Also, as water is a light
molecule there are more molecules per gram, than most similar molecules,
to absorb this energy. Heat absorbed is given out on cooling, so allowing
water to act as a heat reservoir, buffering against changes in
temperature. [Back]

T3 Water has about twice the specific heat
capacity of ice or steam (compare benzene where CP liquid =
1.03 x CP solid).

At its melting point the CPs of ice-Ih
and water are 38 J mol-1 K-1 and 76 J mol-1
K-1 respectively. The CP's of the other ices may be
up to about 40% higher (ice-three) than that
of ice-1h but are all significantly lower than liquid water [606].
The specific heats of polar molecules do increase considerably on melting
but water shows a particularly large increase. As water is heated, much of
the energy is used to bend the hydrogen bonds; a factor not available in
the solid or gaseous phase. This extra energy causes the specific heat to
be greater in liquid water. The presence of this large specific heat
offers strong support for the extensive nature of the hydrogen-bonded
network of liquid water. [Back]

T4 The specific heat capacity (CP)
has a minimum at 36°C.

It is usual for the specific heats of liquids to increase with
increased temperature at all temperatures.

The (isobaric; also called isopiestic) specific heat capacity (CP)
has a shallow minimum at about 36°C (D2O ~120°C) with a
particularly steep negative slope below 0°C [15,
67]. The water cluster
equilibrium shifts towards less structure
(for example,
CS) and higher enthalpy as the
temperature is raised. CP is the heat capacity at constant
pressure defined by
CP = (δH/δT)P <(δS)2>TP
<(δH)2>TPN
(that is, equals change in enthalpy with temperature, and proportional
to the square of the entropy (or enthalpy) fluctuations). The extra
positive δH due to the shift in equilibrium (at low temperatures) as
the temperature is raised causes a higher CP than
otherwise, particularly at supercooling temperatures where a much
larger shift occurs [1353]. This addition
to the CP, as the temperature is lowered, is greater than
the 'natural' fall expected, so causing a minimum to be created. Note
that CV equals CP at the temperature of maximum
density. Usually in liquids CP is more than 20% greater
than CV.

The CV values for
supercooled water may be erroneous, being calculated from
other data and showing an apparent
discontinuity at about -20°C.

It is expected that the large specific heat changes with temperature at
low temperatures will be reduced at higher pressures and this specific
heat-pressure minimum will shift to lower temperatures. The minimum in CP
has been associated with a discontinuity in the Raman depolarization
ratio (that is, perpendicular/parallel polarization) data of degassed
ultrapure water and hence a weak liquid-liquid phase transition at 34.6°C
(5.8 kPa) [1044]. [Back]

T5 The specific heat capacity (CP)
has a maximum at about -45°C.

There are large specific heat changes with temperature at low
temperatures but
deeply supercooled water has lower specific heat at very low
temperatures. At sufficiently low temperature, there must be a maximum
in the specific heat (CP)-temperature relationship, so long
as no phase change occurs. This is expected to lie just below the
minimum temperature accessible on supercooling (232 K, [215]),
although a modeling approach using
TIP5P gives ~250 K [1352]. The
data opposite for supercooled water (upper red
line) is taken from [906]. [Back]

T6 The specific heat capacity (CP)
has a minimum with respect to pressure.

There is a minimum in the heat capacity (CP) of liquid water
with respect to pressure; ~400 MPa at 290 K [606].
This may be explained as due to the break-up of the hydrogen bonding as
the pressure increases below 200 MPa followed by its partial build-up, due
to interpenetrating hydrogen bonded networks, at the higher pressures. [Back]

T7 The heat capacity (CV)
has a maximum.

The CV (the heat capacity at
constant volume, CV = (δU/δT)V) of liquid water is
reported as showing an opposite anomaly, giving a maximum in the
supercooled region (this is not shown in the
calculated values graphed above). The
increase in CP in the supercooled region is because most of the
anomalous enthalpy change is associated with the anomalous volume change.
The decrease in CV in the supercooled region is reported as due
to the decrease in van der Waals non-bonded interactions, due to water's
low density [682]. [Back]

Water has the highest heat of vaporization per gram of any
molecular liquid (2257 J g-1 at boiling point). There is
still considerable hydrogen bonding (~75%) in water at 100°C. As
effectively all these bonds need to be broken (very few indeed
remaining in the gas phase), there is a great deal of energy required
to convert the water to gas, where the water molecules are effectively
separated. The increased hydrogen bonding at lower temperatures causes
higher heats of vaporization (for example, 44.8 kJ mol-1,
at 0°C).

The high heat of vaporization also causes water to have an anomalously
low ebullioscopic constant (that is, effect
of solute on boiling point elevation, 0.51 K kg/mol, compare CCl4
4.95 K kg/mol).Also related is the anomalously
low cryoscopic constant of water. [Back]

T9 High heat of sublimation (51.059 kJ mol-1 at 0°C).

The high heats of fusion and
vaporization combine to give rise to an
anomalously high heat of sublimation. [Back]

Water also has anomalously high entropy of vaporization due to the
hydrogen-bonded order lost on vaporization in addition to the order lost
by virtue of being a liquid changing into a gas. As the
heat of vaporization is also anomalously
high, the ratio (ΔHvap/ΔSvap) is not anomalous.

Interestingly, the entropy of vaporization is inversely related to the
absolute temperature from supercooled water to above 400K (that is, ΔSvap
1/T). [Back]

T11 The thermal conductivity of water is high and rises to a
maximum at about 130°C.

Apart from liquid metals, water has the highest thermal conductivity of
any liquid. For most liquids the thermal conductivity (the rate at which
energy is transferred down a temperature gradient) falls with increasing
temperature but this occurs only above about 130°C in liquid water [188].

As the temperature of water is lowered, the rate at which energy
is transferred is reduced to an ever-increasing extent. Instead of the
energy being transferred between molecules, it is stored in the
hydrogen bonding fluctuations within the increasingly large clusters
that occur at lower temperatures. When the thermal energy is increased
it shifts the
ESCS
equilibrium towards the
CS structure, which possesses
greater flexibility and has a greater number of bent hydrogen bonds,
rather than the transference of kinetic energy. It is likely that
there will be a minimum in the thermal conductivity-temperature
behavior at about -30±15°C as the amount of fully expanded network
increases and in line with that indicated by the much higher value
found for ice 1h. A modeling approach using
TIP5P gives the minimum at ~250 K [1352].

If the density is kept constant the thermal conductivity is
proportional to the square root of the absolute temperature, between
100°C and 400°C [614]. [Back]

Thermal conductivity along the saturation line (liquid-vapor
equilibrium line). Note that the pressure increases with the
temperature, see phase diagram. The
thermal conductivity becomes infinite at the
critical point
[IAPWS].

Water structure and science
(http://www.lsbu.ac.uk/water/explan3.html)

Explanation of the Material
Anomalies of Water (M1-M12)

M1 No aqueous solution is ideal

Ideality depends on the structure of the solvent being unaffected by
the solute. Water is not even close to being a homogeneous phase at the
molecular level. Local clustering will be effected by the presence of
solutes, so changing the nature of the water. Even solutions of HDO in H2O
do not behave ideally. Although most
non-aqueous solutions also show deviations from ideality at higher
concentrations, the deviations that occur in aqueous solutions are
generally much more extensive. [Back]

M2 D2O and T2O differ significantly from H2O
in their physical properties

Normally different isotopic forms of compounds behave very similarly to
each other. The heavier forms of water (D2O where D =
deuterium, 2.0141017780 g mol-1; and T 2O where T =
tritium, 3.0160492675 g mol-1) form stronger hydrogen bonds
than light water (H2O where H = protium, 1.0078250321 g mol-1)
and vibrate less. Hence, they are more ordered than normal water, as shown
by their greater molar volumes. This causes
many of their properties (such as the viscosity, self-diffusion
coefficient, protein solubility and toxicitya
[424]) to be different from those expected
from a simple consideration of their increased mass (for example, the D2O/H2O
viscosity ratio rises from about 1.16 at 100°C to around 2.0 in deeply
supercooled water [23b]. This difference
appears as a shift in the equilibrium position equivalent to a slight
increase in temperature [425]; for example,
viscosity data has been reconciled if the temperatures are shifted by
6.498°C and 8.766°C for D2O and T2O respectively [73].b
H2O is about four-fold stronger as an acid than D2O
at 25°C and H3O+ in H2O is 1.5 times as
strong an acid as D3O+ in D2O.
Remarkably, the difference in the specific heat
minimum between H2O and D2O is over 80°C.
Most of the differences between the behavior of H2O and D2O
may be explained as due to the nuclear quantum effectsi
inherent in the large mass difference between the hydrogen and oxygen
atoms [554]. Although the electron densities
of the different isotopic forms of liquid water have proved, so far, to be
indistinguishable [566], it is expected that
the O-D bond length is shorter than that of O-H due to its smaller
asymmetric vibration and the smaller Bohr radius of D relative to H. This
gives rise to small differences in the size and direction of the dipole
moment between HDO and H 2O [1174],
which further confuses any analysis of the structure of water containing
mixed hydrogen isotopes.

Almost pure H2O and D2O exist but HDO can never
be more than about 50% pure, existing only in the presence of both H2O
and D2O. Mixtures of H2O and D2O
equilibrate to form HDO:
H2O + D2O
2HDO Keq = 3.82, 25°C [609],
ΔH = 129.4 J mol-1 [654]
which is close to a total randomization of the hydrogen atoms (that is,
equal concentrations of HOH, HOD, DOH and DOD giving Keq = 4)
but is reflected in a slight preference for the partitioning of the
deuterium-containing species into the more extensive and stronger
hydrogen-bonded clusters. The Keq decreases with decreased
temperature [126a] and increased hydrogen
bond cooperativity [985]. Even the properties
of HDO deviate from those expected from a consideration of the properties
of H2O and D2O [126b],
with the D-atom preferring to be hydrogen bonded over the H-atom except
where the H-bond is particularly short (as in H5O2+)
[985]. The vibrational
spectrum of HDO is fundamentally different from either H2O
or D2O due to the separation of the two hydroxyl (O-H and O-D)
vibrations in HDO but their combined motion in H2O and D2O.
In HDO the H atom is more reactive and more easily dissociated than the D
atom. As hydrogen bonding is a property of at least two water molecules,
isotopic mixtures contain many differently paired (and more extensive)
species each of which may present different properties to those in natural
liquid water. It is clear that care must be taken over extrapolating the
properties of H2O/D2O mixtures (often used in
neutron scattering and vibrational spectroscopic studies) to those of
normal liquid water (that is, 99.97% H2O). For example, D2O
is preferentially found at hydrophilic interfaces [1342].

Even H218O behaves differently from H216O
due to reduced quantum translational motions, reducing the size of the
first shell local hydrogen-bonded tetrahedron but leaving the non-bonded
water distances almost the same [1035].
Although D2O has similar mass (only 0.04% heavier than H218O),
its behavior much more affected by the isotopic substitution, due to the
altered mass distribution influencing its librations and hence the local
environment of both the first and second aqueous shells [1035].
[Back]

M3 Liquid H2O and D 2O differ significantly
in their phase behavior.

The phase behavior of liquid H2O and D2O differ,
with the triple point of D2O being 3.82°C and 49 Pa higher than
that of H2O, their vapor pressure curves crossing at 221°C and
the critical point of D2O being 3.25°C and 393 kPa lower [1007].
This isotope effect has its origins in the reduced zero point vibration of
D2O that reduces its van der Waals volume (by about 1%) and its
associated repulsive effect within the hydrogen bonds at lower
temperatures, so increasing the D2O-D2O hydrogen
bond strength.c At higher
temperatures the transition to the excited state is more easily
accomplished in D2O (~2450 cm-1, relative to H2O
~3280 cm-1). Due to the asymmetry of the vibration, this
increases D2O's effective van der Waals volume and reverses the
relative repulsive effect, so reducing the D2O-D2O
hydrogen bond strength at higher temperatures.d

As the Keq decreases with decreased temperature [126a]
and increased hydrogen bond cooperativity [985]
(see above), at temperatures close to 0 K
this may mean that H2O and D2O may form separate
phases and are no longer in equilibrium [985].
[Back]

M4 Solutes have varying effects on properties such as density and
viscosity

Solutes will interfere with the cluster equilibrium by favoring either
open or collapsed structures. Any effect will cause the physical
properties of the solution, such as density or viscosity, to change.
Solutes have a lower than expected effect on both the
cryoscopic (that is, effect of solute on freezing
point depression, 1.86 K kg mol-1, compare CCl4
30 K kg mol-1) and ebullioscopic
constants due to water's low molar mass and high heats of fusion and
evaporation respectively. [Back]

M5 The solubilities of non-polar gases in water decrease with
increasing temperature to a minimum and then rise.e

Non-polar gases are poorly soluble in water. Most gaseous solutes
dissolve more in most solvents as the temperature is raised. However,
non-polar gasses are much more soluble in water at low temperatures than
would be expected from their solubility behavior at high temperatures.

The solubilities of the noble gases is shown opposite [IAPWS,
1166] and given below. Their hydration
may be considered as the sum of two processes: (A) the endothermic
opening of a clathrate pocket in the water, and (B) the exothermic
placement of a molecule in that pocket, due to the multiple van der
Waals interactions (for example, krypton dissolved in water is
surrounded by a clathrate cage with 20 Kr···OH2 such
interactions [1357]). In water at low
temperatures, the energy required by process (A) is very small as such
pockets may be easily formed within the water clustering (by
CS
ES)f.

Using the noble gases to investigate the solvation of non-polar gases
is useful as they are spherically symmetrical and have low polarizability,
whereas shape and polarizability may confuse the hydration of other gases.
The solubility of the noble gases increases considerably as the
temperature is lowered. Their enthalpy and entropy of hydration become
more negative as their fit into the water dodecahedral clathrate improves.

He

Ne

Ar

Kr

Xe

Rn

Atomic number

2

10

18

36

54

86

Atomic radius, Å [1167]

1.08

1.21

1.64

1.78

1.96

2.11

ΔG° of solution in H2O at 25°C, kJ mol-1
[1296]

29.41

29.03

26.25

24.80

23.42

ΔH° of solution in H2O at 25°C, kJ mol-1
[1296]

-0.59

-3.80

-11.98

-15.29

-18.99

ΔS° of solution in H2O at 25°C, J mol-1
K-1 [1296]

-100.6

-110.1

-128.2

-134.5

-142.2

Solubility, mM, 5°C, 101,325 Pa [1166]

H2O

0.41

0.53

2.11

4.20

8.21

18.83

D2O

0.49

0.61

2.38

4.61

8.91

20.41

Solubility minima, °C [IAPWS,
678]

H2O

30

50

90

108

110

D2O

53

53

98

108

116

Oxygen (O2) and nitrogen (N2) molecules behave
similarly (solubility minima at N2 74°C and O2 94°C,
IAPWS), although their solubilities are low
(O2, 1.92 mM in H2O, 2.14 mM in D2O; N2,
0.94 in H2O, 1.05 mM in D2O; all at 5°C, 101,325 Pa
[1168]). The greater solubility of O2
over N2, in spite of its lesser clathrate forming ability [1168]
has been proposed due to its formation of weak hydrogen bonds to water [1168].
g

The solubilization process is therefore exothermic (that is, has
negative ΔH) and (as predicted by Le Chatelier's principle) solubility
decreases with temperature rise. At high temperatures (often requiring
high pressure) the natural clustering is much reduced causing greater
energy to be required for opening of the pocket in the water. The
solubilization process therefore becomes endothermic and (as predicted by
Le Chatelier's principle) solubility goes through a minimum before
increasing with temperature rise (being fully miscible under supercritical
conditions).

The more attractive the solute-water van der Waals interactions
(due both to atomic number dependency and goodness of fit within the
clathrate pocket), the greater the inherent exothermic nature of the
process and therefore the higher the temperature minimum (see Table
above) and the greater the temperature range of negative temperature
solubility coefficient. Similarly Henry's constants (= partial
pressure/mole fraction;h
represents volatility, see opposite) exhibit increasing maxima with
increasing size (the maxima are the same as the solubility minima
above).

The poor solubility of non-polar gases in water, in spite of the
negative enthalpy change on dissolution, is due to positive free energy
change (+ve ΔG) attributed to the large negative entropy change (-ve TΔS)
caused by the structural enhancement of the water (ES)
clusters; a conclusion reinforced by the enhanced
heat capacity of these solutions (+ve Cp, characteristic
of a decrease in the degrees of freedom of the water solvent). This
structural enhancement may include the fixing of the cluster centers,
preventing the randomizing flickering between clusters otherwise evident,
as well as ordering the inner dodecahedral water shells surrounding the
solute molecules. There is also a reduction in volume (-ve ΔV) showing a
reduction in the unoccupied space within the water solvent and also
indicative of the gases occupying the pre-existing, if collapsed,
clathrate sites. Counter-intuitively in spite of it forming
stronger hydrogen bonds, D2O is a
better solvent than H2O for non-polar gases, as it is a more
static molecule and more easily forms the
ES water clustering. Therefore D2O
can accommodate the guest molecules more easily without breaking its
hydrogen bonds [874]. Addition of
positively hydrating salts (for example, LiCl)
that destroy the water low-density
ES clustering reduce the solubility
('salt out') of the non-polar gases whereas
hydrophobic hydrating salts (for example, tetramethylammonium
chloride) that increase water low-density
ES clustering stability also
increase non-polar gas solubility ('salt in'). Small non-polar organic
molecules also behave similarly to non-polar gases, but their increased
size alters the clathrate structuring. Thus benzene has a solubility
minimum, at a lower temperature than expected from above, at about 20°C [210].

Interestingly, the change in solubility of non-polar gases with respect
to their diameters has a maximum (and their free energy of hydration has a
minimum) when diameters are about the same as that of the dodecahedral
cavities (that is, ~4.5 Å) in the icosahedral
network [196]. The solubility behavior
of larger hydrophobic molecules is
discussed briefly elsewhere. It should also be noted that the solvent
properties of liquid superheated water also change with temperature as
water's dielectric permittivity reduces
towards that of common organic solvents as the temperature rises towards
its critical point.

Even though the amount of air (that is, N2 + O2 +
Ar) dissolved in water is very low, it is sufficient to lower the density
of water by almost 5 ppm (that is, 0.0005%) at 0°C [870].

It should be clear from the above discussion that the solubility of
non-polar gases, in water at its boiling point, is not zero; an error
propagated by some text-books.

The solubility of gases (and other solutes such as salts) in ice is
very low. This explains the usefulness of freeze-thaw operations under
reduced pressure for degassing water. [Back]

M6 The dielectric constant of water is high (78.4
at 25°C)

Polar molecules, where the centers of positive and negative charge are
separated, possess dipole moment. This means
that in an applied electric field, polar molecules tend to align
themselves with the field. Although water is a polar molecule, its
hydrogen-bonded network tends to oppose this alignment. The degree to
which a substance does this is called its dielectric constant (permittivity).
Because water possesses a hydrogen bonded network that transmits polarity
shifts extensively through rapid and linked collective changes in the
orientation of its hydrogen bonds, it has a high dielectric constant. This
allows it to act as a solvent for ionic compounds, where the attractive
electric field between the oppositely charged ions is
reduced by about 80-fold, allowing thermal
motion to separate the ions into solution. On cooling, as the water
network strengthens and water's dipole moment increases, the
dielectric of liquid water climbs to 87.9
(0°C), increasing on conversion to ice then increasing further as the ice
is cooled. On heating, the dielectric constant drops, and liquid water
becomes far less polar, down to a value of about 6 at the
critical point. The dielectric constant
similarly reduces if the hydrogen bonding is broken by other means such as
strong electric fields but not with pressure. The change in dielectric
with temperature gives rise to considerable and anomalous changes in its
solubilization and partition properties with temperature, which are
particularly noticeable in superheated water [610]
where the dielectric is low, and in supercooled water where the dielectric
is high and increases (107.7 at -35°C) even as the density decreases.
Pressure increases the dielectric constant (101.42 at 0°C and 500 MPa),
due to its effect on the density.

Perhaps the high dielectric constant of water should not be considered
anomalous as other small polar molecules (with higher dipole moments) form
liquids also having high dielectric constants (see below).The
ratio dielectric constant/(dipole moment)2 is often also
reckoned, by others, to be anomalously high in liquid water (but note that
the gas-phase, rather than liquid, dipole moments are used for comparing
these substances). Although high, clearly molecules with zero dipole
moment (e.g. CCl4) have infinite such values.

M7 The dielectric constant shows a temperature maximum.

Anomalous dielectric behavior of water is found over a range of
microwave frequencies between about 2 and 100 GHz whereby the real
(ε') and/or the imaginary (ε'') part of the
complex dielectric constant increase then decrease with
increasing temperature. Examples at two close frequencies for liquid
(including supercooled) water are shown opposite [588].
This may be understood by noting the shifts with
temperature of the maximum frequency of microwave absorption
and the dielectric permittivity.

Analysis of the complex
permittivity gives a discontinuity at about 30°C [1045].
[Back]

M8 Proton and hydroxide ion mobilities are anomalously fast in an
electric field.

The ionic mobilities of hydrogen ions and hydroxide ions at 361.9 and
206.5 (nm s-1)/(V m-1) at 25°C are very high
compared with values for other small ions such as lithium (40.1 (nm s-1)/(V
m-1)) and fluoride (57.0 (nm s-1)/(V m-1))
ions. This is explained by the Grotthuss mechanism.

The limiting ionic conductivities are related (= mobility x charge x
Faraday) and their values for hydrogen ions and hydroxide ions, at 349.19
and 199.24 S cm2 mol-1 at 25°C [737],
are similarly very high compared with values for other small ions such as
lithium (38.7 S cm2 mol-1) and fluoride (55.4 S cm2
mol-1) ions. [Back]

M9 The electrical conductivity of water rises to a maximum at about
230°C and then falls.

The electrical conductivity of water
increases with temperature up to about 230°C due mainly to its
increased ionization producing higher
concentrations of the highly conducting H+ and OH-
ions, which reach maximum concentrations at about 250°C [IAPWS].
Above this temperature, for liquid water in equilibrium with the
vapor, the density is much reduced (for
example, 0.7 g cm-3 at 300°C) and this reduces the ability
for ionization. Proton mobility decreases
above 149°C due to lowered amounts of 'Zundel'
cations (that is, H5O2+) [1061].

Note that the pKw also
reaches a maximum value at about 250°C in line with that of the
hydrogen ion concentration [IAPWS].

Opposite is shown the great increase in the resistivity (=
1/conductivity) of water at low temperatures [737];
extrapolated values are shown in dashed blue.
Interestingly, the electrical conductivity
of water increases on degassing [711].
Together these properties support the formation of
ES clusters at low
temperatures and in the presence of non-polar gases, which involve
localized and limited isotropic hydrogen bonding and so prevent
lengthy directed proton movements. [Back]

M10 Acidity constants of weak acids show temperature minima.

An interesting anomaly concerns the changes in the pKa
with temperature of many weak acids. As an example, opposite is shown
this for the second ionization of phosphoric
acid; H2PO4-H+
+ HPO42-. Such changes are due to a combination
of factors including changes in the dielectric (high temperatures
increasing the pKa) and hydrogen bonding (low temperatures
increasing the pKa). [Back]

M11 X-ray diffraction shows an unusually detailed structure

This is shown elsewhere and is simply
explained by the presence of ordered
clustering within the liquid phase. [Back]

M12 Under high pressure water molecules move further away from each
other with increasing pressure.

When liquid water is put under pressure (below about 200 MPa) the
water molecules approach their neighbors more closely, as might be
expected from the increase in density. However, if the pressure is
increased from about 200 to 400 MPa, the average distance between
neighboring water molecules increases [51].
At higher pressures the distances reduce again (but less so) with
increasing pressure. A similar and corroborative behavior is seen with
the O-H stretch vibration frequency (v1),
which increases with pressure between about 200 to 400 MPa [533]
whilst reducing with pressure at higher or lower pressures. The O-H
stretch data has been confirmed at 23°C but not found at 52°C,
indicating that it requires larger clusters to be recognized [824].

The explanation for all these effects is that there appears to be an
increase in interpenetration of hydrogen bonded networks at about 200 MPa
(at 290 K); interpenetration of hydrogen bonded clusters being preferred
over more extreme bending or breaking of the hydrogen bonds. When liquid
water is put under pressure (below about 200 MPa) the water molecules
approach their neighbors more closely, as might be expected from the
increase in density.

This is similar to what happens in the high density ices where, for
example, ice-seven (with two interpenetrating
cubic ice lattices) under a pressure of over
2200 MPa (density 1.65 g cm-3) has an average O····O nearest
neighbor distance about 3.5% greater than that in
cubic ice (density 0.92 g cm-3 at 0.1 MPa). Thus the
density of ice-seven is somewhat less than
twice the density of cubic ice (that is,
2x0.92/(1.035)3 = 1.65 g cm-3). [Back]

Footnotes

a D2O is toxic to many organisms at high levels
(20%-100% D2O, where it affects many processes including
mitosis and membrane function) but is not generally considered harmful at
much lower levels where it is used in human physiological research. There
is some evidence to show that artificially reducing its natural abundance
in water (0.03% w/w) may have positive effects on the health of organisms
[424]. [Back]

b This method for reconciling the data works poorly at low
temperatures [1049]. [Back]

c The reduced zero point energy when switching D-atoms for
H-atoms from free to hydrogen bonded positions within water clusters has
been shown due to the energetic consequences of the lowering of the bend
and torsional bond energies which are greater than the raising of the
stretching bond energy [986]. [Back]

d Also contributing to this effect are the relative isotopic
differences between the zero point energies of the liquid and gaseous
phases. Librational vibrations (due to
hydrogen bonding) release energy when the phase changes from liquid to
gaseous (where they are absent) with H2O librations (being
greater) releasing more energy and so increasing the volatility of H2O
relative to D2O at lower temperatures. Opposite effects are
apparent at higher temperatures where there is less hydrogen bonding but
energy still needs to be supplied to provide for the increased zero point
vibrational energy of the stretch vibrations
(the gaseous stretch vibrations being more energetic than those for the
liquid phase) [992]. [Back]

e In many gaseous-solute solvent systems (for
example, N2 in CCl4) , the solubility increases with
temperature increase. Although solubility decreases with temperature
increase is encountered with some other solute-solvent combinations (for
example, methane in n-heptane), the behavior is a more general
property of water and deserves comment. [Back]

f There is evidence [157,
269, 274] that
the first (clathrate) shell possesses stronger hydrogen bonding and this
weakens the hydrogen bonding out to the next shell. [Back]

g The formation of O=O···H-OH hydrogen bonds may be
seen as the first stage in the natural low-level formation of oxygen redox
products (for example, H2O2) in water. As the ratio
of O2/N2 solubilities has a maximum at 290 K, there
is indication that partial clathrate cages may be responsible for the
polarization that encourages the hydrogen bond formation. [Back]

h Henry's constant = partial pressure/mole fraction (KH)
may be described by the following equation
.
where p is the partial pressure of the solute in the gas, X is the solute
mole fraction, R is the gas constant, T is the absolute temperature, VH2O
is the molar volume of water and μ is the
temperature-dependent excess chemical potential of hydration for the
solute [1276]. [Back]

i Nuclear quantum effects concern the different
energies of the vibrational states. The bonds involving the deuterium atom
(being about twice as heavy as the protium atom) vibrate with less
amplitude and frequency. Nuclear quantum effects are seen particularly in
differences in their zero point energy; the vibrational energy that
remains at close to absolute zero. [Back]

Water structure and science
(http://www.lsbu.ac.uk/water/explan5.html)

Explanation of the Physical
Anomalies of Water (P1-P12)

F1 High viscosity (0.89 cP, compare
pentane 0.22 cP, at 25°C)

The viscosity of a liquid is determined by the ease with which
molecules can move relative to each other. It depends on the forces
holding the molecules together (cohesiveness). This cohesivity is large in
water due to its extensive three-dimensional hydrogen bonding. It should
be noted that although the viscosity of water is high, it is not so high
that it causes too much difficulty being moved around within organisms.
The Arrhenius energy of activation for viscous flow is similar to the
hydrogen bond energy (H2O, 21.5 kJ mol-1; D2O,
24.7 kJ mol-1; T2O, 26.2 kJ mol-1, all
calculated from [73]; all at 0°C and all more
than doubling at -30°C). [Back]

F2 Large viscosity increase as the
temperature is lowered.

The increase in the viscosity with lower temperatures is
particularly noticeable within supercooled water (see opposite). The
water cluster equilibrium shifts towards
the more open structure (for example,
ES) as the temperature is
lowered. This structure is formed by stronger hydrogen bonding. In
turn, this creates larger clusters and reduces the ease of movement
(increasing viscosity). [Back]

F3 Viscosity decreases with pressure (at temperatures below 33°C)

Viscous flow occurs by molecules moving through the voids that exist
between them. As the pressure increases, the volume decreases and the
volume of these voids reduces, so normally increasing pressure increases
the viscosity.

Water's pressure-viscosity behavior [534]
can be explained by the increased pressure (up to about 150 MPa)
causing deformation, so reducing the strength of the hydrogen-bonded
network, which is also partially responsible for the viscosity. This
reduction in cohesivity more than compensates for the reduced void
volume. It is thus a direct consequence of the
balance between hydrogen bonding effects and the van der Waals
dispersion forces [558] in water;
hydrogen bonding prevailing at lower temperatures and pressures. At
higher pressures (and densities), the balance
between hydrogen bonding effects and the van der Waals dispersion
forces is tipped in favor of the dispersion forces and the remaining
hydrogen bonds are stronger due to the
closer proximity of the contributing oxygen atoms [655].
Viscosity, then, increases with pressure. The dashed line (opposite)
indicates the viscosity minima

The variation of viscosity with pressure and temperature has been
used as evidence that the viscosity is determined more by the extent
of hydrogen bonding rather than hydrogen bonding strength [824].

Self-diffusion is also affected by pressure where (at low
temperatures) both the translational and rotational motion of water
anomalously increase as the pressure increases (see
below). [Back]

F4 Large diffusion decrease as the temperature is lowered.

Diffusion may be generally described by the Stokes-Einstein equation
for translational diffusion [806],
and the Stokes-Einstein-Debye equation for rotational diffusion,
,where Dt and Dr are the
translational and rotational diffusivities respectively, R is the
gas constant,
N is
Avogadro's number, η is dynamic viscosity and r is
water's molecular radius. The values for
self-diffusion are greatly reduced at lower temperatures where they
anomalously decrease as the density decreases (see
below). This is unsurprising as these diffusion terms are
approximately proportional to the reciprocal of the viscosity, and
viscosity anomalously increases at lower
temperatures. The inverse relationship between water diffusivity and
dynamic viscosity, and the ratio of translational to rotational
diffusivity, are almost independent of temperature between about
-35°C and +100°C. However there is a strong divergence from these
relationships, and their ratio [1040c], at
lower, supercooled, temperatures (at 225 K [1040a])
due to the differential effects of clustering [807]
caused by the presence of both low and higher density aqueous phases [1040].
Although such behavior is expected of liquids close to their glass
transition, that is not the case with water where it occurs well above the
glass-transition temperature.

The diffusion equations (above) give unexpectedly good estimates for
the radius of the water molecule (r = 1.1 Å, 25°C)a
given that the equations were derived for large spherical particles.

The activation energy for this diffusion increases to about the
equivalent of two hydrogen bonds (44.4 kJ mol-1) at 238 K
where the diffusion coefficient is 1.58 x 10-10 m2
s-1 [653]. The importance of
this activation energy disappears above about 315 K, when it appears
to be less than the thermal energy [1295].
Thus, the main reason for the low diffusion at low temperatures is the
three-dimensional hydrogen bond network.

As shown below, this anomalous diffusional behavior is not present when
water diffuses in nitromethane in the absence of hydrogen bonding [652].

[Back]

F5 At low temperatures, the self-diffusion of water increases as
the density and pressure increase.

The increase in self-diffusion with density (within the range of
about 0.9 g cm-3 up to about 1.1 g cm-3, at low
temperatures) is in contrast to normal liquids where increasing
density decreases self-diffusion as the molecules restrict each
other's movements. The density increase may be due to increasing
temperature, below 4°C, at atmospheric pressure or due to increasing
pressure at low temperatures. Liquids normally show reduced
self-diffusion when they are squeezed but water at 0°C increases its
diffusivity by 8% under a pressure of about 200 MPa [226]
and the diffusivity of supercooled water at -30°C increases by 60%
with a similar pressure increase. Further increase in pressure reduces
the diffusivity in common with the behavior of other liquids. The
movement of water becomes restricted at low temperatures as the more
open (lower density) structure produced on cooling (see
above) is formed by stronger and more complete hydrogen
bonding, which reduces the self-diffusion. The strength of the
hydrogen bonding is a controlling influence in this anomalous region,
where the hydrogen bond angles and the inter-molecular distances are
strongly coupled and this order decreases on compression [169]
due to the collapse of
ES structures to
CS structures. Simulation
studies have shown that self-diffusion goes through a minimum as the
density of water is reduced below about 0.9 g cm-3 followed
by an increase with further density reduction, as might be expected
from most liquids [402], due to the
disruption of the network at low density as the now-stretched hydrogen
bonds are broken [626]. The maximum in
the self diffusion is brought about as at even higher pressures there
is an increased packing density due to the gradual phase transition to
interpenetrating hydrogen bonded networks.

Data for these tables was calculated froma
the IAPWS viscosity data [540].
The dashed lines indicate the maxima.

For the same reasons, the molecular rotational movement of water
(reciprocal rotational relaxation time) also varies in direct proportion
to the changes in self-diffusion (translational movement). [Back]

F6 The thermal diffusivity rises to a maximum at about 0.8 GPa.

The thermal diffusivity (),b
which arises from vibrations in the water network [713],
shows less anomalous temperature and pressure behavior than might be
expected due to the dependence on the anomalously-behaving, but
counteractive, thermal conductivity,
density and
specific heat capacity. There is, however, a steep increase in
thermal diffusivity at low temperatures (see left, 25°C) and a maximum
in the low-temperature thermal diffusivity - pressure behavior at
about 0.8 GPa [614].

It is likely that there will be a minimum in the thermal
diffusivity-temperature behavior at about -30±15°C at atmospheric pressure
in line with changes in the specific heat (CP)
and thermal conductivity. A modeling approach
using
TIP5P gives the minimum at ~250 K [1352].
[Back]

F7 High surface tension (72.75 mJ/m2,
cf. CCl4 26.6 mJ/m2 at 20°C)

Surface tension (surface free energy,
)
at a gas liquid interface is produced by the attraction between the
molecules being directed away from the surface as surface molecules
are more attracted to the molecules within the liquid than they are to
molecules of the gas at the surface. In contrast, molecules of water
in the bulk are equally attracted in all directions. In order to
achieve the greatest possible interaction energy, surface tension
causes the maximum number of surface molecules to enter the bulk of
the liquid and, hence, the surface area is minimized.

Water has an abnormally high surface tensionc
and surface enthalpyd with an abnormally tightly packed
surface compared to bulk liquid water.e
Water molecules at the liquid-gas surface
have lost potential hydrogen bonds directed at the gas phase and are
pulled towards the underlying bulk liquid water by the remaining stronger
hydrogen bonds [214]. Energy is required to
increase the surface area (removing a molecule from a well hydrogen bonded
interior bulk water to the lesser hydrogen bonded surface), so it is
minimized and held under tension. As the forces between the water
molecules are several and relatively large on a per-mass basis, compared
to those between most other molecules, and the water molecules are very
small, the surface tension is large. Lowering the temperature greatly
increases the hydrogen bonding in the bulk causing increased surface
tension.

Although there is no clear anomaly in the surface
tension/temperature behavior
[IAPWS], there are inflection
points at about -6°C [865] and 250°C [427].
The inflection in the data at about -6°C has been explained by use of
a two-state mixture model involving low-density and higher density
water clusters [866].

Surface tension
changes differently from bulk water properties due to surface
enrichment with water clusters.

The greater than expected drop in surface tension
with temperature increase (0.155 mJ m-2 K-1
at 25°C) is one of the highest known and similar to that of the liquid
metals. It has been quantitatively explained using spherically symmetrical
water clustering [376]. The thermodynamic
change in surface tension with pressure is
very high at 25°C [1280]. e

It is interesting to note that surfactants lower the surface tension
because they prefer to sit in the surface, attracting the surface water
molecules in competition to the bulk water hydrogen bonding and so
reducing the net forces away from the surface (that is, the surface
tension).

The high surface tension of water endows it with some rather unexpected
properties. Thus, water drops may rise up an inclined plate, against
gravity, if subjected to symmetrical vibrations of about 100 Hz [1311].
This is due to the unequal changes in contact angle at the top and bottom
surfaces, creating upwards forces greater than that due to gravity, and
the non-linear friction effects. Also, if a small drop of water (typically
1 mm diameter) is coated in a fine (typically 20 μm diameter) hydrophobic
dust then the drop can roll and bounce without leakage [225],
and the aqueous spheres can even float on water. Capillarity holds the
dust at the air-liquid interface with the elasticity being due to the high
surface tension. [Back]

The affinity of chaotropic ions for the
expanded and weakly hydrogen bonded
surface water structure (aided by the excess of 'lone pair' electrons
directed towards the bulk [594]) may help
explain the shallow minima in their surface tension at very low ionic
concentrations (that is, the Jones-Ray effect [674];
first dismissed erroneously as an artifact by Irving Langmuir). For
example, at low concentration (< 1 mM) the surface tension of KCl
solutions drops (~-0.01% change) with increasing concentration. The
increase in surface tension with higher concentrations of salt is thought
due to the relative depletion of salt within the surface, which means that
when ions do absorb at the surface a depletion layer must be created
deeper in. Also, higher concentrations of such salts must
disproportionately increase the bulk salt concentration so adding to the
attractive forces on the surface water molecules, consequently adding to
the increase in the surface tension. Kosmotropic
cations and anions prefer to be fully hydrated in the bulk liquid
water and so increase the surface tension by the latter mechanism at all
concentrations. This partitioning is noticeable in NaCl solutions, such as
seawater; the weakly chaotropic Cl- occupying surface sites
whereas the weakly kosmotropic Na+ only resides in the bulk
water [928]. The polarizability of large
chaotropic anions (such as I-) is accentuated due to the
asymmetric solvent distribution at the surface and increases the strength
of chaotrope-solvent interactions when at the surface [989].
Similarly to chaotropic ions, hydroxyl
radicals also prefer to reside at air-water interfaces [939];
the radicals donating one hydrogen bond but accepting less than two [943].
The lesser hydration energy of OH- relative to H3O+,
results in OH- preferring the surface over the H3O+,
which also has some, but less, preference for the surface [1205,1308],
and biases a pure aqueous interface to give it a negative potential [1205c,
1308]. The preference of H3O+
for the surface in acid solution (due to its surface active nature, as its
O atom is not hydrogen bonded) is shown by the drop in surface tension
with HCl, HNO3 and HClO4 (but not H2SO4)
acid concentration. [Back]

F9 Some salts prevent the coalescence of small bubbles.

Higher concentrations (often about 0.1M) of many, but not all, salts
prevent the coalescence of small gas bubbles (recently reviewed [672])
in contrast to the expectation from the raised surface tension and reduced
surface charge double layer effects (DLVO
theory). Higher critical concentrations are required for smaller bubble
size [599]. This is the reason behind the
foam that is found on the seas (salt water) but not on lakes (fresh
water). The salts do not directly follow the
Hofmeister effects with both the anion and cation being important
with one preferentially closer to the interface than the other; for
example, excess hydrogen ions [1205] tend to
negate the effect of halides [622]. The
explanation for this unexpected phenomenon is that bubble coalescence
entails a reduction in the net
gas-liquid surface, which acts as a sufficiently more favorable
environment for the one out of a pair of ions rather than the bulk when
their concentration is higher than a critical value. It has been proposed
that anions and cations may be divided into two groups α and β with α
cations (Na+, K+, Mg2+) and β anions (ClO4-,
CH3CO2-, SCN-) ) avoiding the
surface and α anions (OH-, Cl-, SO42-)
and β cations (H+, (CH3)4N+)
attracted to the interface; αα and ββ anion-cation pairs then cause
inhibition of bubble coalescence whereas αβ and βα pairs do not [1305].
These groupings do not behave as bulk-phase ionic
kosmotropes and chaotropes, which indicates the different
properties of bulk water to that at the
gas-liquid surface. It is likely that the ions reside in the
interfacial region, between the exterior surface layer and interior bulk
water molecules, where the hydrogen bonding is naturally most disrupted [605].
A similar phenomenon is the bubble (cavity) attachment to microscopic salt
particles used in microflotation, where chaotropic anions encourage
bubble formation [758].

Interestingly, the concentration of salt in our bodies corresponds to
the minimum required for optimal prevention of bubble coalescence [622].
As small bubbles are much less harmful than large bubbles, this fact is
very useful. [Back]

Footnotes

a If the equation for 'slip boundary' solutes, where the
solute diffusion does not involve the fixed shell of solvent molecules
assumed in the above equation, is used
then the water hydrodynamic radius is close to correct at 1.64 Å at 25°C.
[Back]

bAt temperatures between 100°C and 400°C,
the thermal diffusivity scales as the square root of the absolute
temperature (Diffusivity/√T density
[614]). [Back]

c A freshly exposed surface of water would be
expected to have much higher surface energy (~0.180 J m-2 [1255]
). [Back]

d Surface enthalpy (also known as the total surface
energy) may be calculated from the binding energy lost per unit surface
area (= molecules per surface area x binding energy lost per molecule. If
the surface is only half occupied with water molecules that have lost
about a third of their hydrogen bonds, the surface enthalpy should be =
0.5 x (1019 molecule m-2) x (1/6.022x1023
mol molecule-1) x 1/3 x (45 kJ mol-1) = ~0.125 J m-2
(compare with the actual value of 0.118 J m-2). [Back]

e The influence of pressure on the surface tension of
water, as with other liquids, is not straightforward. There are two clear
effects. Firstly, the thermodynamic relationship relating surface tension
to pressure
has been shown to equal the change in volume associated with forming more
surface,
[1283].
may be taken as a measure of the difference in density of the liquid in
the bulk compared with that at its surface and is therefore generally
positive (that is, the surface tension should increase with pressure about
+0.7 mJ m-2 MPa-1 for water at 25°C). The pressure
coefficient of the surface tension (
= surface enthalpy/internal+external pressure,
= 0.702 nm at 25°C) is much generally higher than for other liquids; for
example, methanol (0.159 nm), diethyl ether (0.176 nm), benzene (0.178 nm)
and even mercury (0.398 nm) [1280]. This high
value for water indicates that the density at the surface of water is more
similar to the bulk liquid than occurs in most other liquids (see
the thermodynamic derivatization).
Anomalously amongst liquids, the densities of surface and bulk water are
equal at 3.97 °C (at atmospheric pressure, as calculated from the
equations given in [1280]) and below this
temperature the bulk liquid is less dense than the surface liquid.

The thermodynamic relationship does not hold for real liquid-gas
systems, however, where the application of pressure will cause water vapor
to condense and gas molecules to adsorb on to the liquid-gas interface.
The adsorption of gas molecules to the surface of liquid water lowers the
surface tension by a greater extent than the thermodynamic effect outlined
above (except perhaps for helium). Thus, the surface tension of water, in
contact with other molecules in the gas phase, drops with increase in
pressure due to the surface activity of surface-absorbed gas molecules [1282].
The extent of this lowering depends upon the gas involved and is much
greater for hydrophilic gasses, such as CO2 (-7.7 mJ m-2
MPa-1) , than nonpolar gasses such as N2 and O2
(-0.8 mJ m-2 MPa-1). [Back]